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DECION MAKINGANALYSIS/DECISION

MAKING TREEANALYSIS

DR. JAMELA R. USMAN-PASAGI

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WHAT IS THE TOOL ALL ABOUT?

A decision treeis a decision support tool thatuses a tree-lie !raph or "odel o# decisions andtheir possi$le conse%uences&

includin! chance e'ent outco"es& resource costs&and utilit(. It is one )a( to displa( an al!orith".

Decision trees are co""onl( used in operations

research& speci*call( in decision anal(sis& to helpidenti#( a strate!( "ost liel( to reach a !oal& $utare also a popular tool in "achine learnin!.

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WHY USE THE TOOL?

+onductin! anal(sis o# decision "ain! underuncertaint( usin! decision trees ser'es se'eralpurposes.

,. A decision tree is a 'isual representation o# adecision situation and hence aidsco""unication.

/. 0he $ranches o# a tree e1plicitl( sho) all those#actors )ithin the anal(sis that are consideredrele'ant to the decision and i"plicitl( those thatare not.

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WHY USE THE TOOL?

2. A decision tree !enerall( captures the idea that i#di3erent decisions )ere to $e taen then thestructural nature o# a situation and hence o# the"odel "a( ha'e chan!ed dra"aticall(.

4. A decision tree allo)s #or #or)ard and $ac)ardcalculation paths to happen and hence thechoice o# the correct decision to tae is "adeauto"aticall(.

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WHEN TO USE THE TOOL?

Decision trees ha'e a natural 5i# ... then ... else ...5 constructionthat "aes it *t easil( into a pro!ra""atic structure. 0he( alsoare )ell suited to cate!ori6ation pro$le"s )here attri$utes or#eatures are s(ste"aticall( checed to deter"ine a *nal cate!or(.

E'aluation o# $rand e1pansion opportunities #or a $usiness usin!historical sales data

Deter"ination o# liel( $u(ers o# a product usin! de"o!raphicdata to ena$le tar!etin! o# li"ited ad'ertise"ent $ud!et

Prediction o# lielihood o# de#ault #or applicant $orro)ers usin!

predicti'e "odels !enerated #ro" historical data 7elp )ith prioriti6ation o# e"er!enc( roo" patient treat"ent

usin! a predicti'e "odel $ased on #actors such as a!e& $loodpressure& !ender& location and se'erit( o# pain& and other"easure"ents

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HOW TO USE THE TOOL?

S%uares represent decisions(ou can "ae. 0he linesthat co"e out o# eachs%uare on its ri!ht sho) allthe a'aila$le distinct optionsthat can $e selected at thatdecision anal(sis point.

+ircles sho) 'ariouscircu"stances that ha'euncertain outco"es 8ore1a"ple& so"e t(pes o#e'ents that "a( a3ect (ouon a !i'en path.

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HOW TO USE THE TOOL?

0he lines that co"e outo# each circle denotepossi$le outco"es o#

that uncontrolla$lecircu"stance.

9rite do)n a$o'e eachsuch line in the

decision tree (our $est!uesses #orpro$a$ilities o# thosedi3erent outco"es.

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HOW TO USE THE TOOL?

Each path that can $e#ollo)ed alon! thedecision tree& #ro" le#t

to ri!ht& leads to so"especi*c outco"e.

:ou need to descri$ethose end results in

ter"s o# (our "aincriteria #or ;ud!in! theresults o# (ourdecisions..

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HOW TO USE THE TOOL?

Ideall(& (ou )ill assi!neach end outco"e a%uantitati'e "easureo# the o'erall total$ene*t (ou )illrecei'e #ro" thatoutco"e (ou can

e1press it as apercei'ed "onetar('alue.

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HOW TO USE THE TOOL?

Ideall(& (ou )ill assi!neach end outco"e a%uantitati'e "easureo# the o'erall total$ene*t (ou )illrecei'e #ro" thatoutco"e (ou can

e1press it as apercei'ed "onetar('alue.

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HOW TO USE THE TOOL?

No) (ou ha'e a co"pletedecision "ain! tree )ithspeci*c nu"$ers #or $oththe pro$a$ilities o# the

uncertain e'ents and the$ene*t "easuresdesira$ilit( o# each endresult.

At this sta!e the tree can!i'e (ou "ore speci*creco""endation on )hat)ould $e (our $estchoices.

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HOW TO USE THE TOOL?

In particular& #or each choicethat (ou control at the decisionpoints sho)n $( s%uares& (oucan calculate the o'erall

desira$ilit( o# that choice.

Just su" the $ene*t "easureso# all the end outco"es that can$e traced $ac to that choice

'ia one path or another&)ei!hted $( the pro$a$ilities o#the correspondin! paths. 0his)ill sho) (ou the pre#erredchoice the one )ith the hi!hesto'erall desira$ilit(.

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HOW TO USE THE TOOL?

I# (ou ha'e "ore than onedecision point& (ou need todo that calculation #or thedecisions that are at the

latest sta!es *rst. Identi#(the choice that !i'es thehi!hest o'erall desira$ilit(and lea'e onl( that $ranchre"o'in! the decision

point. Do the sa"e )ith the

re"ainin! s%uares& )orin!(our )a( to the le#t to the*rst decision point in these%uence.

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EAM!LE

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HOW TO USE THE TOOL?

CANDY SHO!

OR

LEMONADE STAND

Let

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HOW TO USE THE TOOL?

Let

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HOW TO USE THE TOOL?

Cut )hat i# the cand( shop and (our le"onade standhad *#t( percent chance o# success and also had a*#t( percent chance o# #ailure>

? success

? #ail

? success

? #ail

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I# (our cand( shop is a success& (ou )ould earn P,??.i# )as a #ailure& (ou )ould lose P2?.n the other hand& i# (our le"onade stand is a

success& (ou )ould earn P@?. i# )as a #ailure& (ou)ould lose P,?. 9hich one do (ou choose no)>

? success

? #ail

? success

? #ail

P,??

-P2?

P@?

-P,?

9hich onedo (ouchooseno)>

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Use this si"ple #or"ula percenta!e o# chance 1earnin!s.8or cand( shop& ? "ultiplied $( P,?? i#success#ul plus ? "ultiplied $( FP2? i# #ailure.8or le"onade stand& ? "ultiplied $( P@? i#success#ul plus ? "ultiplied $( FP,? i# #ailure.? success

? #ail

? success

? #ail

P,??

-P2?

P@?

-P,?

? P,?? ?-P2? H P2

? P@? ?-P,? H P4?

9hich onedo (ou

chooseno)>

LEMNADE S0AND

)ith P4?B

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0he results are=8or cand( shop= P28or le"onade stand=P4?. 9hich one do (ou chooseno)>

? success

? #ail

? success

? #ail

P,??

-P2?

P@?

-P,?

? P,?? ?-P2? H P2

? P@? ?-P,? H P4?

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!ROBLEM TO SOL"E

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MARY#S $ACTORY

Mar( is a "ana!er o# a !ad!et #actor(. 7er #actor( has

$een %uite success#ul the past three (ears. She is)onderin! )hether or not it is a !ood idea to e1pand her#actor( this (ear. 0he cost to e1pand her #actor( is ,.M.I# she does nothin! and the econo"( sta(s !ood and peoplecontinue to $u( lots o# !ad!ets she e1pects 2M in re'enue

)hile onl( ,M i# the econo"( is $ad.I# she e1pands the #actor(& she e1pects to recei'e KM i#econo"( is !ood and /M i# econo"( is $ad.

She also assu"es that there is a 4? chance o# a !ood

econo"( and a K? chance o# a $ad econo"(.Dr%& % Decision Tree s'o&in( t'ese c'oices)

$ORMULA* +,ercent%(e o- c'%nce . reen0e1 2 cost

W'ere3 cost4 S5)6 M +i- to e.,%nd1 7 cost4 8 +i- not

to e.,%nd1

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THANK YOU)

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ANSWER

Expand Factory

Cost = $1.5 M

Dont Expand Factory

Cost = $0

40 % Chance of a Good Economy

rof!t = $"M

"0% Chance #ad Economy

rof!t = $M

Good Economy 40%&

rof!t = $'M

#ad Economy "0%&

rof!t = $1M

NPVExpand= (.4(6) + .6(2)) 1.5 = $2.1M

NPVNo Expand= .4(3) + .6(1) = $1.8M

$2.1 > 1.8, th!"o! #o %ho&d xpand th "a'to!#

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